and we write \(\mathcal {E}_i:=\mathcal {E}^{(i)}/\mathcal {E}^{(i-1)}\)  for the successive subquotients; this filtration is the HN filtration of \(\mathcal {E}\)  if \(q_{\mathcal {E}} \in Y_\tau ^{ss}\) . The limit of \(\lambda (t) \cdot q_{\mathcal {E}}\)  as \(t \rightarrow 0\)  corresponds to the associated graded sheaf \(\operatorname{gr}(\mathcal {E}^{(\bullet )})=\oplus _i \mathcal {E}_i\)  of the filtration (REF ); see [1]} and [2]}. Thus the morphism \(p_\tau : Y_\tau ^{ss} \rightarrow Z_\tau ^{ss}\)  takes a sheaf to its HN-graded sheaf. In particular, we have the following statements concerning the minimal weight space for \(\lambda _\tau \)  (see also Propositions REF  and REF ).
